Alright, let's work through 6697 times 8610 step by step
6697 × 8610 = 8610 × (6697)
+ 8610 × 7 that is equal 60270
+ 8610 × 90 yielding 774900
+ 8610 × 600 which equals 5166000
+ 8610 × 6000 yielding 51660000

= 57661170
